Multiplication principle - high school - math problems

Birthday paradox How large must the group of people be so that the probability that two people have a birthday on the same day of the year is greater than 90%?

The test The test contains four questions, and there are five different answers to each of them, of which only one is correct, the others are incorrect. What is the probability that a student who does not know the answer to any question will guess the right answer

Fall sum or same Find the probability that if you roll two dice, it will fall the sum of 10, or the same number will fall on both dice.

Birth Let's assume that the probability of the birth of a boy and a girl in the family is the same. What is the probability that in a family with five children, the youngest and oldest child is a boy?

The university At a certain university, 25% of students are in the business faculty. Of the students in the business faculty, 66% are males. However, only 52% of all students at the university are male. a. What is the probability that a student selected at random in t

Divide How many different ways can three people divide 7 pears and 5 apples?

Beads How many ways can we thread 4 red, 5 blue, and 6 yellow beads onto a thread?

Cube construction A 2×2×2 cube is to be constructed using 4 white and 4 black unit cube. How many different cubes can be constructed in this way? ( Two cubes are not different if one can be obtained by rotating the other. )

Boys and girls There are 20 boys and 10 girls in the class. How many different dance pairs can we make of them?

Two groups The group of 10 girls should be divided into two groups with at least 4 girls in each group. How many ways can this be done?

Graduation party There are 15 boys and 12 girls at the graduation party. Determine how many four couples can be selected.

One three We throw two dice. What is the probability that max one three falls?

Menu On the menu are 12 kinds of meal. How many ways can we choose four different meals into the daily menu?